RoboguruRoboguru
SD

Tentukan himpunan penyelesaian dari persamaan-persamaan trigonometri berikut! a. sin (3x−21​π)=sin 31​π, 0≤x≤2π

Pertanyaan

Tentukan himpunan penyelesaian dari persamaan-persamaan trigonometri berikut!

a. sin space open parentheses 3 x minus 1 half straight pi close parentheses equals sin space 1 third straight pi comma space 0 less or equal than straight x less or equal than 2 straight pi  

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

himpunan penyelesaiannya adalah open curly brackets 5 over 18 straight pi comma space 1 third straight pi comma space 17 over 18 straight pi comma space straight pi comma space 29 over 18 straight pi comma space 5 over 3 straight pi close curly brackets.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah begin bold style stretchy left curly bracket 5 over 18 pi comma space 1 third pi comma space 17 over 18 pi comma space pi comma space 29 over 18 pi comma space 5 over 3 pi stretchy right curly bracket end style.

Persamaan Trigonometri Dasar

Ingat persamaan trigonometri dasar berikut:

Jika sin space x equals sin space alpha, nilai x equals alpha plus k times 2 straight pi atau x equals open parentheses straight pi minus straight alpha close parentheses plus k times 2 straight pi.

Diketahui sin space open parentheses 3 x minus 1 half straight pi close parentheses equals sin space 1 third straight pi comma space 0 less or equal than straight x less or equal than 2 straight pi, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 3 x minus 1 half pi close parentheses end cell equals cell sin space 1 third pi end cell row cell 3 x minus 1 half pi end cell equals cell 1 third pi plus k times 2 pi end cell row cell 3 x end cell equals cell 1 half pi plus 1 third pi plus k times 2 pi end cell row cell 3 x end cell equals cell fraction numerator 3 pi plus 2 pi over denominator 6 end fraction plus k times 2 pi end cell row x equals cell 5 over 18 pi plus k times 2 over 3 pi end cell end table 

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 3 x minus 1 half pi close parentheses end cell equals cell sin space 1 third pi end cell row cell 3 x minus 1 half pi end cell equals cell open parentheses pi minus 1 third pi close parentheses plus k times 2 pi end cell row cell 3 x minus 1 half pi end cell equals cell 2 over 3 pi plus k times 2 pi end cell row cell 3 x end cell equals cell 1 half pi plus 2 over 3 pi plus k times 2 pi end cell row cell 3 x end cell equals cell fraction numerator 2 pi plus 4 pi over denominator 6 end fraction plus k times 2 pi end cell row x equals cell 6 over 18 pi plus k times 2 over 3 pi end cell row blank equals cell 1 third pi plus k times 2 over 3 pi end cell end table 

Diperoleh:

k equals 0 rightwards arrow x equals 5 over 18 pi plus 0 times 2 over 3 pi equals 5 over 18 pi space left parenthesis straight M right parenthesis space atau k equals 0 rightwards arrow x equals 1 third pi plus 0 times 2 over 3 pi equals 1 third pi space left parenthesis straight M right parenthesis k equals 1 rightwards arrow x equals 5 over 18 pi plus 1 times 2 over 3 pi equals 17 over 18 pi space left parenthesis straight M right parenthesis space atau k equals 1 rightwards arrow x equals 1 third pi plus 1 times 2 over 3 pi equals pi space left parenthesis straight M right parenthesis k equals 2 rightwards arrow x equals 5 over 18 pi plus 2 times 2 over 3 pi equals 29 over 18 pi space left parenthesis straight M right parenthesis space atau k equals 2 rightwards arrow x equals 1 third pi plus 2 times 2 over 3 pi equals 5 over 3 pi space left parenthesis straight M right parenthesis 

Keterangan:

M (Memenuhi)

Dengan demikian, himpunan penyelesaiannya adalah open curly brackets 5 over 18 straight pi comma space 1 third straight pi comma space 17 over 18 straight pi comma space straight pi comma space 29 over 18 straight pi comma space 5 over 3 straight pi close curly brackets.

59

0.0 (0 rating)

Pertanyaan serupa

Tentukan himpunan penyelesaian dari setiap persamaan trigonometri di bawah ini. a. sin (x−30)∘=sin 15∘, 0∘≤x≤360∘

218

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia